Elementary mathematical theory for stress singularities at the vertex of plane infinite wedges

Abstract

A particular singular problem in the class of plane linear elasticity theory that plays an important role in the development of linear elastic fracture mechanics (LEFM) is reviewed and mathematically studied. The specific problem is started with consideration of a planar wedge having stress-free on both radial edges but the remainder subjected to in-plane loading at the far-field. Employing the semi-inverse method together with the Fadle eigenfunction expansion technique, its solution can be written in terms of Airy stress function satisfying the two-dimensional biharmonic governing differential equation. Further analysis leads to a special case of crack problems, which is in the field of elastic fracture mechanics.